The difficulty with your question is that there isn't really an over arching Native American culture. North America was home to a couple hundred distinct tribes with their own beliefs and religions. There was some overlap, but generally they are all different. I think the best option for you is to choose a particular culture group and go from there. But to give something of an answer, I'm studying to be an anthropologist and Native American culture is a field that I am very interested, and the 2 creation myths I know off hand are that of the Haudenosaunee (Iroquois) and the Sioux.

Haudenosaunee: In the beginning there was no earth. Just a vast ocean. In the sky was an island upon which the Sky People lived. On this island nobody was born or died and there was no such thing as sadness. One day one of the Sky Women discovered she was pregnant. This angered her husband and, in his rage, he uprooted the great tree which was in the center of the island and which produced lights (as the sun had yet to be created). The Sky Woman went and looked through the hole that this created and could see the vast ocean and was curious, but her husband pushed her and she fell through the hole. (Another version claims that the Sky Woman was sent down wrapped in light by the Ruler of the Sky People in order to create land below, not pushed by her angry husband) Now in that ocean, multitudes of water animals lived and they immediately came to the Sky Woman's aid. The animals knew that she would require earth to stand on and all of the animals tried diving to the ocean floor to get some but they all failed. Then the lowly muskrat dove and gathered some and the animals spread it on a turtle's back. The turtle grew and grew until he was the size of North America and Sky Woman rested there. Eventually she gave birth to her twins, the good Sapling and the evil Flint. Sapling was born the normal way, but Flint was cruel and impatient and forced his way out through his mother's underarm, killing her. After her death the new island was covered in darkness, so Sapling made the sun from her face. Flint then created a great darkness that would chase her from the west (night). Sapling then made stars and the moon from his mother's breasts and placed them in the night sky. He then buried her body in the earth (hence mother earth, from whom all life comes). The crow arrived and, in his ear, Sapling found a corn kernel and planted it, sowing the first crop. Crow stilll flies around corn fields, protecting the corn, but taking a share for himself as well. Sapling created all humans and the good things in the world and, had it been just him, life would be simple. But Flint created hardships, he put cruelty into men's hearts, he put the small, sharp bones in fish, he made inedible berries and plants, and he made the harsh winters that the Haudenosaunee homeland (Western New York) are known for.

The Sioux: In the beginning were 2 beings Inian (rock) and Wakhan Tanka (the creator). Inian wanted to show his compassion and spread himself to become the earth or Makka, but in doing so lost a lot of blood, which became water. This caused Inian to shrivel up and became hard, and he begins losing his powers. The water cannot retain his powers, and Skan (the motion of the universe/ flow of water) was created. Makka complains to Inian that everything is cold and dark, and so he creates Anpao, the Dawn. As Anpao's red light was not enough for Maka, Inyan creates Wi, the Sun to bring light. Wi is married to the moon and they have a daughter, the shooting star. Meanwhile there are two beings called Old Man and Old Woman and they have a daughter Ite who is married to the Wind. With Wind she has 4 sons, the four winds (North wind, South wind, East wind, West wind). ktomi, the spider, convinces Ike to have an affair with the sun and she does. The affair is found out and Moon leaves the Sun (creating day and night) and Ike has a fifth son, the Tornado. Wind and the four sons leave and Ite now feels lonely so she gets Iktome to go find more people. He travels underground in the shape of a wolf and finds Tokahe, the first man. Tokahe emerges from underground (at Wind Cave in South Dakota) and marvels at all the beauty and Ike teaches him how to cook, hunt, fish, make clothing and build the teepee.

There are many versions of both of these tales (especially the Sioux one since the Sioux aren't an individual tribe, but are just categorized as such by white people. Siouxan describes the language which is spoken by many tribes from Ohio to the Rockies and north into Canada (and some other places scattered offside of there) the Lakota, Dakota, Miniconjou, Brule, Yankton, etc. Hope this helps. If you want to private message me I'm happy to talk about Native American stuff